While not specifically restricted to grandchildren, there are a variety of
scholarships based on a student’s ancestry and heritage.
One example is the Order of Sons of Italy in America, which requires at least one Italian or Italian American grandparent.
The US Bureau of Indian Affairs also awards aid based on having at least 1/4 native american
blood (i.e., at least one grandparent is full-blooded).

The Edward M. Kennedy Serve America Act (HR 1388) authorizes the
Senior Scholarships program. This program provides $1,000 education
awards for people age 55 or older who volunteer for 350 or more hours
a year. These awards may be used for the volunteer’s own education or
transferred to a child, foster child or grandchild. Congress must
still vote to appropriate funding for the program as part of the
President’s FY2010 budget.

Contributing to College Savings Plans

Approximately a quarter to a third of grandparents help their
grandchildren save for college through 529 college savings plans,
gifts or other means.

529 college savings plans, prepaid tuition plans, Coverdell education
savings accounts and Series I and certain Series EE savings bonds are
tax-advantaged ways of saving for college. Distributions are tax-free
when used to pay for qualified higher education expenses and are not
counted as income or resources when evaluating eligibility for federal
need-based student aid. Many states allow you to detect all or part of
your contribution to the state 529 college savings plan on your state
income tax return. You can contribute up to the annual gift tax
exclusion ($13,000 in 2009 per grandparent per beneficiary) without
incurring any gift taxes. 529 college savings plans also allow for
larger lump sum contributions using 5-year gift tax averaging.

When a grandparent owns a college savings plan, it is sometimes
disregarded when calculating a student’s eligibility for need-based
aid. However, this does not necessarily increase the amount of student
aid the grandchild will get as compared with parent or child ownership
of the college savings plan. For example, section 529 college savings
plans, prepaid tuition plans and Coverdell education savings accounts
are not reported as assets on the Free Application for Federal Student
Aid (FAFSA) of a dependent student if they are owned by a grandparent
of the student. This is due to a change enacted by the
College Cost Reduction and Access Act of 2007. The change was
effective starting in 2009-10.

The specific legislative language was:

(3) A qualified education benefit shall be considered an asset of --
(A) the student if the student is an independent student; or
(B) the parent if the student is a dependent student, regardless
of whether the owner of the account is the student or the parent.